MRI in soils: determination of water concent changes due to root water uptake by means of a multi-slice-multi-echo sequence (MSME)

Root water uptake by ricinus communis (castor bean) in fine sand was investigated using MRI with multiecho sampling. Before starting the experiments the plants germinated and grew for 3 weeks in a cylindrical container with a diameter of 9 cm. Immediately before the MRI experiments started, the containers were water-saturated and sealed, so water content changes were only caused by root water uptake. In continuation of a preceding work, where we applied SPRITE we tested a multi-echo multi-slice sequence (MSME). In this approach, the water content was imaged by setting TE = 6.76 ms and nE = 128 with an isotropic resolution of 3.1mm. We calculated the water content maps by biexponential fitting of the multi-slice echo train data and normalisation on reference cuvettes filled with glass beads and 1 mM NiCl2 solution. The water content determination was validated by comparing to mean gravimetric water content measurements. By coregistration with the root architecture, visualised by a 3D fast spin echo sequence (RARE), we conclude that the largest water content changes occurred in the neighbourhood of the roots and in the upper layers of the soil

A Lagrangian stochastic model for the transport in statistically homogeneous porous media

A new type of stochastic simulation models is developed for solving transport problems in saturated porous media which is based on a generalized Langevin stochastic differential equation. A detailed derivation of the model is presented in the case when the hydraulic conductivity is assumed to be a random field with a lognormal distribution, being statistically isotropic in space. To construct a model consistent with this statistical information, we use the well-mixed condition which relates the structure of the Langevin equation and the probability density function of the Eulerian velocity field. Numerical simulations of various statistical characteristics like the mean displacement, the displacement covariance tensor and the Lagrangian correlation function are presented. These results are compared against the conventional random displacement method